To solve this problem, we need to calculate two things: the arithmetic mean and the median of the given scores, and then find their difference.

Step 1: Calculate the Arithmetic Mean

The arithmetic mean (average) is calculated by dividing the sum of all values by the number of values. Here, we have the scores: 19, 4, 17, 7, 15, 2, 18, 11, 15, 17, 19, 4, 3, 2, 6, 9.

First, calculate the sum of all scores:

19 + 4 + 17 + 7 + 15 + 2 + 18 + 11 + 15 + 17 + 19 + 4 + 3 + 2 + 6 + 9 = 168

Now, divide the sum by the number of students (16) to find the mean:

\text{Mean} = \frac{168}{16} = 10.5

Step 2: Calculate the Median

The median is the middle value in a list when the numbers are sorted in ascending order. For an even number of observations, as in this case, the median is the average of the two middle numbers.

First, sort the scores: 2, 2, 3, 4, 4, 6, 7, 9, 11, 15, 15, 17, 17, 18, 19, 19.

Since there are 16 scores, the median will be the average of the 8th and 9th values:

The 8th and 9th values are 9 and 11, respectively.

\text{Median} = \frac{9 + 11}{2} = 10

Step 3: Find the Difference

The difference between the arithmetic mean and the median is:

10.5 - 10 = 0.5

Conclusion: The difference between the arithmetic mean and the median of the scores is 0.5. Thus, the correct answer is 0.5.